{{no footnotes, date=May 2015
A fitness function is a particular type of
objective function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cos ...
that is used to summarise, as a single
figure of merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. Examples
*Clock rate of a CPU
* Calories per serving
*Contrast ratio of an LCD
*Frequency response of a speaker
* ...
, how close a given design solution is to achieving the set aims. Fitness functions are used in
genetic programming
In artificial intelligence, genetic programming (GP) is a technique of evolving programs, starting from a population of unfit (usually random) programs, fit for a particular task by applying operations analogous to natural genetic processes to t ...
and
genetic algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...
s to guide simulations towards optimal design solutions.
Genetic programming and algorithms
In particular, in the fields of
genetic programming
In artificial intelligence, genetic programming (GP) is a technique of evolving programs, starting from a population of unfit (usually random) programs, fit for a particular task by applying operations analogous to natural genetic processes to t ...
and
genetic algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...
s, each design solution is commonly represented as a string of numbers (referred to as a
chromosome
A chromosome is a long DNA molecule with part or all of the genetic material of an organism. In most chromosomes the very long thin DNA fibers are coated with packaging proteins; in eukaryotic cells the most important of these proteins are ...
). After each round of testing, or simulation, the idea is to delete the ''n'' worst design solutions, and to
breed
A breed is a specific group of domestic animals having homogeneous appearance (phenotype), homogeneous behavior, and/or other characteristics that distinguish it from other organisms of the same species. In literature, there exist several slig ...
''n'' new ones from the best design solutions. Each design solution, therefore, needs to be awarded a figure of merit, to indicate how close it came to meeting the overall specification, and this is generated by applying the fitness function to the test, or simulation, results obtained from that solution.
The reason that genetic algorithms cannot be considered to be a lazy way of performing design work is precisely because of the effort involved in designing a workable fitness function. Even though it is no longer the human designer, but the computer which comes up with the final design, it is still the human designer who has to design the fitness function. If this is designed badly, the algorithm will either converge on an inappropriate solution, or will have difficulty converging at all.
The fitness function should not only correlate closely with the designer's goal, but it also should be computationally efficient. Speed of execution is very important, as a typical genetic algorithm must be iterated many times in order to produce a usable result for a non-trivial problem.
Fitness approximation
Fitness approximationY. JinA comprehensive survey of fitness approximation in evolutionary computation ''Soft Computing'', 9:3–12, 2005 aims to approximate the objective or fitness functions in evolutionary optimization by building up machine l ...
may be appropriate, especially in the following cases:
* Fitness computation time of a single solution is extremely high
* Precise model for fitness computation is missing
* The fitness function is uncertain or noisy.
Two main classes of fitness functions exist: one where the fitness function does not change, as in optimizing a fixed function or testing with a fixed set of test cases; and one where the fitness function is mutable, as in
niche differentiation
In ecology, niche differentiation (also known as niche segregation, niche separation and niche partitioning) refers to the process by which competing species use the environment differently in a way that helps them to coexist. The competitive excl ...
or
co-evolving
In biology, coevolution occurs when two or more species reciprocally affect each other's evolution through the process of natural selection. The term sometimes is used for two traits in the same species affecting each other's evolution, as well ...
the set of test cases.
Another way of looking at fitness functions is in terms of a
fitness landscape
Fitness may refer to:
* Physical fitness, a state of health and well-being of the body
* Fitness (biology), an individual's ability to propagate its genes
* Fitness (cereal), a brand of breakfast cereals and granola bars
* ''Fitness'' (magazine), ...
, which shows the fitness for each possible chromosome.
Definition of the fitness function is not straightforward in many cases and often is performed iteratively if the fittest solutions produced by genetic algorithms are not what is desired.
Interactive genetic algorithms Interactive evolutionary computation (IEC) or aesthetic selection is a general term for methods of evolutionary computation that use human evaluation. Usually human evaluation is necessary when the form of fitness function is not known (for example ...
address this difficulty by outsourcing evaluation to external agents which are normally humans.
Test functions for optimization
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as:
* Convergence rate.
* Precision.
* Robustness.
* General performance.
Here some test functions are ...
*
Loss function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost ...
PDF
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ...
PDF
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ...
), A review of fitness functions used in
evolutionary robotics Evolutionary robotics is an embodied approach to Artificial Intelligence (AI) in which robots are automatically designed using Darwinian principles of natural selection. The design of a robot, or a subsystem of a robot such as a neural controller, ...